The Seagulls turned in a good all-round performance with goals from Dean Hammond and Andrea Orlandi securing maximum points.
And the Uruguayan even had the luxury of resting strikers Craig Mackail-Smith and Ashley Barnes, instead giving rare starts to Stephen Dobbie and Will Hoskins.
"We got a clean sheet, scored a couple of goals so I've no complaints," Poyet said. "It was a good, professional display. We needed to keep patient and make it difficult for the opposition."
"Dobbie and Hoskins were desperate to play and this was an opportunity for them to come into the side and impress. I think they both had good games without being spectacular."
Brighton visit arch-rivals Crystal Palace on Saturday and Poyet admitted this comfortable victory was a perfect way to go into such an eagerly-awaited clash.
"I hope it will be a proper game with no problems," he said. "The fans do enjoy those kinds of games."